1. Field of Invention
This invention relates to the gambling casino card game of Twenty-One, also known as Blackjack, specifically to a method of dealing the cards to eliminate player skill from the game.
2. Description of Prior Art
It is common knowledge that the card game of Twenty-One, also known as Blackjack, is unique among all casino gambling games because the casino's winning "edge" is not fixed, as it is in other games such as Craps or Roulette, but varies with each play of a card, so that the player's chances of winning fluctuate significantly from one game to the next. Since the rules of play allow the player to make a series of decisions which directly affect the outcome of the hand, a skillful player can adjust his betting and play to take the most advantage of favorable situations while risking the least in unfavorable ones.
The two main factors that determine the player's chances of winning the hand is what cards are left in the deck at the start of that hand and how the hand is played. Both of these depend upon the player's knowledge of the composition of the deck from which that game is dealt. As certain cards are removed from the deck during prior game play and dealing, the player's chances of being dealt various combinations from the remaining cards increases or decreases, sometimes giving the casino an advantage over the player and sometimes giving the player an advantage over the casino. If the player places large wagers when his chances of winning are greater and small wagers when his chances of winning are lower, in the long run the player will come out ahead. Knowing the chances of winning before each hand is dealt, at the time the wager is placed, depends upon the player keeping track of the cards as they are dealt by means of some card-counting system.
Knowledge of the composition of the deck is not only a guide to wagering, but is vital to successful game play. Edward Thorp, a university mathematics professor, was the first to use an advanced electronic computer to mathematically determine the best possible play for any situation a player may face, based upon the player's initial two-card holding, the value of the dealer's one face-up card, and the known composition of the full deck. He formulated these optimal playing decisions into a simple set of rules he called the "Basic Strategy". For examples: When the player holds a 16 or less and the dealer shows a 7, the dealer's probability of drawing to a 17-21 is 0.74 (where 0=never happens and 1.00=always happens), meaning that nearly 3/4 of the time the player will lose by standing on his holding. Therefore, when the dealer shows a 7 and the player holds 16 or less, the player should draw to try to improve his holding. But if the player's 16 is made up of two 8's, the player should "split" the pair since the probability of the player drawing to 17-21 when holding an 8 is 0.76, and he is therefore more likely to beat the dealer by drawing separately to each 8 rather than to the 16 total; or if the player holds an 11 and the dealer shows a 7, the player shouls "double down" since the probability of reaching 17-21 with a one-card draw to an 11 is 0.79 and he is therefore more likely to beat the dealer who shows a 7. Similarly, when the dealer shows an Ace and the player holds a 20 made up of two 10's (a very likely winner if the dealer doesn't have a 21), the probability of winning the Insurance bet is 0.29--where the Insurance pays 2 to 1, in 100 games the player will receive 58 bet units for his likely 29 wins and lose 71 bet units, giving the casino a 13% advantage! Therefore the player must not insure a 20. But if he holds two low cards, say an 8 and a 6, the probability of his winning the Insurance bet is 0.33, giving the casino only about a 1% advantage; if the player is playing two hands and elects to stand on a 17 in the second hand which is made up of a 9 and an 8, then the probability of the Insurance win becomes 0.34, giving the player a 2% advantage! The Insurance wager is now advantageous!.
Where in a single-deck game with standard rules of play, the casino enjoys an overall advantage over players of about 6%, a player using the Basic Strategy can gain a net advantage of about 1% over the casino, which can increase to over 15% (or even 100%) when the deck is favorable (as revealed by "card-counting").
The standard method of dealing makes it easy for the player to know the composition of the deck with near exactness and so can confidently use the Basic Strategy: first, the dealer shuffles the full deck, then he completes the cut of the deck where a player has indicated, after which the player removes the top card from the deck and typically sets it aside to start a discard pile (called "burning" a card). After each player has placed his wager, the dealer deals out the game in the normal way. All cards used in the game are eventually exposed before the dealer deposits them face-down on the discard pile, setting the stage for the deal of the next game in which the remainder of the deck will be used. Typically, after several games have been played but before the deck is exhausted, the remainder deck is added to the discard pile (restoring the deck to wholeness), and now using the entire discard pile, the dealer will start the next cycle of shuffling, cutting and "burning" before dealing out the next succession of games. In fact, at any time the dealer wishes he may reshuffle all the cards for the next round of games.
FIG. 1 schematically shows the flow of cards in the prior-art dealing method. Of particular significance is the fact that with this method of dealing the players know the composition of the active deck in advance of placing a bet or playing the game.
Through extensive analysis on the computer, Thorp had discovered that the percentage of 10's against other cards measured the degree of favorability--a full single deck contains 36 no-10's and 16 10's, a ratio of 2.25 to 1, and when through card play that ratio became less than 2,25 to 1, the remainder deck was proportionately "richer" in 10's and therefor more favorable to the player. This measurement required that the player keep a double count: first, before the used cards are scooped up by the dealer and placed on the discard pile, the player must count how many 10's and other cards have been played in the first round and second, the player must subtract these from the 36-to-16 ratio with which the deck began; this process must be repeated for each game.
Of course, the "count" was most advantageous to the player if the remainder deck was played down to the very last card so that the player not only knew the ratio (the degree of favorability for betting) but also knew exactly what cards remain in the deck and therefore knew exactly how to play his hand.
Thorp published his findings, which become a best-selling book. This book inflamed the avaraice of gamblers averywhere since it told exactly how to surely "beat the dealer". The operating principle was easy to understand. Basic Strategy was most valid for the first hand dealt from the shuffled deck. As cards were dealt, the deck's composition was altered and so were the probabilities on which sound play tactics depended. Therefore it was important to keep track of the changing character of the deck by noticing which cards were dealt and, by subtraction from the number of those known to previously exist in the deck, know which cards remain to be dealt. As the deck dwindled, more than modifying the decisions of play, Thorp modified the size of his bets. When the deck was "rich" in high-cards (favorable to the player but likely to force the dealer to "bust" and therefore lose), Thorp multiplied his bets.
When Thorp showed that it was possible to win at Twenty-One by using Basic Strategy and card counting, an increasing number of players began to win in the casinos. The casinos' initial panicky response was to alter the rules of play so as to deny players certain advantageous play options. This gross tactic discouraged all players and, when the consequent erosion of business became apparent, casinos restored the rules and elected to substitute other tactics: first, the deck would no longer be played completely (so that players would not have the advantage of "counting down the deck"), i.e., all cards would be reshuffled together well before the active deck was exhausted (or whenever the dealer wished, as shown in FIG. 1), and second, multiple decks were substituted for the single deck formerly used, both to make "counting" more burdensome and consequently less attractive to all but the most dedicated players, and to provide the casino with a greater advantage (a four-deck game added 0.54% to the casino's "edge"). Even though players knew from Thorp's work that the single-deck game was most favorable, the small advantage gained by the casino with multi-deck games did not discourage game play. Enterprising player/mathematicians simply devised other methods of card-counting which were more suited to handling multi-deck games than Thorp's complicated system, and equally effective.
In a later edition of his book, Thorp endorsed a method called "simple point-count" which, with certain variations is still in use. In this method, low cards (2,3,4,5,6) are counted as "+1" as each card is seen to fall during game play and high cards (10,A) are counted as "-1" as each is seen to fall; the intermediate cards (7,8,9) are counted as "0". A running cumulative count of the exposed cards is maintained. With full decks, the count starts and ends at 0. For examples: if 5,5,3,8 are seen to fall, the running cumulative count is +3, and if A,10,10,9,8,8,10,A,A are seen to fall, the running cumulative count would be -6. The cumulative count measures the high-card "richness" in the remainder deck--when it is a high plus number, the remainder deck is "rich" in high cards (favoring the player) and when it is a high minus number, the remainder deck is "rich" in low cards (favoring the dealer). Thorp recommended that the player bet 1 unit if the point-count total is zero or minus,and if the point-count is plus, bet as many units as the point-count total. Thorp also recommended certain changes in his Basic Strategy such as only when the cumulative point-count is greater then +8 should the player take "Insurance" (normally a poor bet with a full deck); when the deck shows a cumulative point-count of -6 or greater minus (there are many small cards in the deck), and the dealer shows a 7 or more, the player should restrict doubling to an 11 holding only, and not split Aces but draw (with a full deck, doubling down on 9 or 10 is recommended, particularly if the dealer shows 2 through 6, and Aces should always be split).
In response to continued player wins despite early shuffles and multi-deck use, the casinos resorted to the additional tactic of barring recognized "card counters", a practise which continues. None of these tactics can totally defeat skilled "card counters" because so long as the standard method of dealing, shown in FIG. 1, is used, players would know the total composition of the active deck(s) in advance of the deal and during game play with a high degree of certainty; they would be able to wager and exercise the various play options so as to maximize wins and minimize losses. While casinos can change the rules of play to benefit themselves (at the risk of discouraging game play and loss of profits), they have not yet come up with an economically-viable way to encourage Twenty-One game play while eliminating the player skill factor from determining the outcome of the game.